PROOF.assoc: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1766-1769 of bend-osdev-gf@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&start_line=1766&end_line=1769

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G

def assoc(+a: G.Gf8Bits, +b: G.Gf8Bits, +c: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.mul(G.Gf8Bits.mul(a, b, p), c, p) == G.Gf8Bits.mul(a, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}:
  %dec(a) : {G.Gf8Bits.mul(G.Gf8Bits.mul(_, b, p), c, p) == G.Gf8Bits.mul(a, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}
  %dec(a) : {G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p) == G.Gf8Bits.mul(_, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}
  Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p), G.Gf8Bits.mul(ss(bl(a), ml(basis(), b, p)), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.cong(G.Gf8Bits, G.Gf8Bits, z => G.Gf8Bits.mul(z, c, p), G.Gf8Bits.mul(ss(bl(a), basis()), b, p), ss(bl(a), ml(basis(), b, p)), lin_l(bl(a), basis(), b, p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), ml(basis(), b, p)), c, p), G.Gf8Bits.mul(ss(bl(a), xs(b, p)), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => G.Gf8Bits.mul(ss(bl(a), l), c, p), ml(basis(), b, p), xs(b, p), ml_x(b, p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), xs(b, p)), c, p), ss(bl(a), ml(xs(b, p), c, p)), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), lin_l(bl(a), xs(b, p), c, p), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => ss(bl(a), l), ml(xs(b, p), c, p), xs(G.Gf8Bits.mul(b, c, p), p), mlx_c(b, c, p))))), Equal.sym(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), ss(bl(a), ml(basis(), G.Gf8Bits.mul(b, c, p), p)), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), lin_l(bl(a), basis(), G.Gf8Bits.mul(b, c, p), p), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => ss(bl(a), l), ml(basis(), G.Gf8Bits.mul(b, c, p), p), xs(G.Gf8Bits.mul(b, c, p), p), ml_x(G.Gf8Bits.mul(b, c, p), p)))))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=basis
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=bl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=dec
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=lin_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ml
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ml_x
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=mlx_c
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ss
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=xs
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.mul